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Properties

Label 1200.4.a.v.1.1
Level $1200$
Weight $4$
Character 1200.1
Self dual yes
Analytic conductor $70.802$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1200,4,Mod(1,1200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1200.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1200.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(70.8022920069\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 150)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1200.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.00000 q^{3} -23.0000 q^{7} +9.00000 q^{9} +30.0000 q^{11} +29.0000 q^{13} +78.0000 q^{17} -149.000 q^{19} -69.0000 q^{21} -150.000 q^{23} +27.0000 q^{27} -234.000 q^{29} +217.000 q^{31} +90.0000 q^{33} +146.000 q^{37} +87.0000 q^{39} -156.000 q^{41} +433.000 q^{43} -30.0000 q^{47} +186.000 q^{49} +234.000 q^{51} -552.000 q^{53} -447.000 q^{57} +270.000 q^{59} +275.000 q^{61} -207.000 q^{63} -803.000 q^{67} -450.000 q^{69} -660.000 q^{71} -646.000 q^{73} -690.000 q^{77} -992.000 q^{79} +81.0000 q^{81} +846.000 q^{83} -702.000 q^{87} -1488.00 q^{89} -667.000 q^{91} +651.000 q^{93} -319.000 q^{97} +270.000 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 3.00000 0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −23.0000 −1.24188 −0.620942 − 0.783857i \(-0.713250\pi\)
−0.620942 + 0.783857i \(0.713250\pi\)
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 30.0000 0.822304 0.411152 − 0.911567i \(-0.365127\pi\)
0.411152 + 0.911567i \(0.365127\pi\)
\(12\) 0 0
\(13\) 29.0000 0.618704 0.309352 − 0.950948i \(-0.399888\pi\)
0.309352 + 0.950948i \(0.399888\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 78.0000 1.11281 0.556405 − 0.830911i \(-0.312180\pi\)
0.556405 + 0.830911i \(0.312180\pi\)
\(18\) 0 0
\(19\) −149.000 −1.79910 −0.899551 − 0.436815i \(-0.856106\pi\)
−0.899551 + 0.436815i \(0.856106\pi\)
\(20\) 0 0
\(21\) −69.0000 −0.717002
\(22\) 0 0
\(23\) −150.000 −1.35988 −0.679938 − 0.733269i \(-0.737993\pi\)
−0.679938 + 0.733269i \(0.737993\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −234.000 −1.49837 −0.749185 − 0.662361i \(-0.769554\pi\)
−0.749185 + 0.662361i \(0.769554\pi\)
\(30\) 0 0
\(31\) 217.000 1.25724 0.628619 − 0.777714i \(-0.283621\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0 0
\(33\) 90.0000 0.474757
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 146.000 0.648710 0.324355 − 0.945936i \(-0.394853\pi\)
0.324355 + 0.945936i \(0.394853\pi\)
\(38\) 0 0
\(39\) 87.0000 0.357209
\(40\) 0 0
\(41\) −156.000 −0.594222 −0.297111 − 0.954843i \(-0.596023\pi\)
−0.297111 + 0.954843i \(0.596023\pi\)
\(42\) 0 0
\(43\) 433.000 1.53563 0.767813 − 0.640675i \(-0.221345\pi\)
0.767813 + 0.640675i \(0.221345\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −30.0000 −0.0931053 −0.0465527 − 0.998916i \(-0.514824\pi\)
−0.0465527 + 0.998916i \(0.514824\pi\)
\(48\) 0 0
\(49\) 186.000 0.542274
\(50\) 0 0
\(51\) 234.000 0.642481
\(52\) 0 0
\(53\) −552.000 −1.43062 −0.715312 − 0.698806i \(-0.753715\pi\)
−0.715312 + 0.698806i \(0.753715\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −447.000 −1.03871
\(58\) 0 0
\(59\) 270.000 0.595780 0.297890 − 0.954600i \(-0.403717\pi\)
0.297890 + 0.954600i \(0.403717\pi\)
\(60\) 0 0
\(61\) 275.000 0.577215 0.288608 − 0.957447i \(-0.406808\pi\)
0.288608 + 0.957447i \(0.406808\pi\)
\(62\) 0 0
\(63\) −207.000 −0.413961
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −803.000 −1.46421 −0.732105 − 0.681192i \(-0.761462\pi\)
−0.732105 + 0.681192i \(0.761462\pi\)
\(68\) 0 0
\(69\) −450.000 −0.785125
\(70\) 0 0
\(71\) −660.000 −1.10321 −0.551603 − 0.834107i \(-0.685984\pi\)
−0.551603 + 0.834107i \(0.685984\pi\)
\(72\) 0 0
\(73\) −646.000 −1.03573 −0.517867 − 0.855461i \(-0.673274\pi\)
−0.517867 + 0.855461i \(0.673274\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −690.000 −1.02121
\(78\) 0 0
\(79\) −992.000 −1.41277 −0.706384 − 0.707829i \(-0.749675\pi\)
−0.706384 + 0.707829i \(0.749675\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) 846.000 1.11880 0.559401 − 0.828897i \(-0.311031\pi\)
0.559401 + 0.828897i \(0.311031\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −702.000 −0.865084
\(88\) 0 0
\(89\) −1488.00 −1.77222 −0.886111 − 0.463474i \(-0.846603\pi\)
−0.886111 + 0.463474i \(0.846603\pi\)
\(90\) 0 0
\(91\) −667.000 −0.768358
\(92\) 0 0
\(93\) 651.000 0.725866
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −319.000 −0.333913 −0.166956 − 0.985964i \(-0.553394\pi\)
−0.166956 + 0.985964i \(0.553394\pi\)
\(98\) 0 0
\(99\) 270.000 0.274101
\(100\) 0 0
\(101\) −792.000 −0.780267 −0.390133 − 0.920758i \(-0.627571\pi\)
−0.390133 + 0.920758i \(0.627571\pi\)
\(102\) 0 0
\(103\) −812.000 −0.776784 −0.388392 − 0.921494i \(-0.626969\pi\)
−0.388392 + 0.921494i \(0.626969\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1416.00 1.27934 0.639672 − 0.768648i \(-0.279070\pi\)
0.639672 + 0.768648i \(0.279070\pi\)
\(108\) 0 0
\(109\) −55.0000 −0.0483307 −0.0241653 − 0.999708i \(-0.507693\pi\)
−0.0241653 + 0.999708i \(0.507693\pi\)
\(110\) 0 0
\(111\) 438.000 0.374533
\(112\) 0 0
\(113\) 1404.00 1.16882 0.584412 − 0.811457i \(-0.301325\pi\)
0.584412 + 0.811457i \(0.301325\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 261.000 0.206235
\(118\) 0 0
\(119\) −1794.00 −1.38198
\(120\) 0 0
\(121\) −431.000 −0.323817
\(122\) 0 0
\(123\) −468.000 −0.343074
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −1280.00 −0.894344 −0.447172 − 0.894448i \(-0.647569\pi\)
−0.447172 + 0.894448i \(0.647569\pi\)
\(128\) 0 0
\(129\) 1299.00 0.886594
\(130\) 0 0
\(131\) −480.000 −0.320136 −0.160068 − 0.987106i \(-0.551171\pi\)
−0.160068 + 0.987106i \(0.551171\pi\)
\(132\) 0 0
\(133\) 3427.00 2.23428
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −282.000 −0.175860 −0.0879302 − 0.996127i \(-0.528025\pi\)
−0.0879302 + 0.996127i \(0.528025\pi\)
\(138\) 0 0
\(139\) −1604.00 −0.978773 −0.489387 − 0.872067i \(-0.662779\pi\)
−0.489387 + 0.872067i \(0.662779\pi\)
\(140\) 0 0
\(141\) −90.0000 −0.0537544
\(142\) 0 0
\(143\) 870.000 0.508763
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 558.000 0.313082
\(148\) 0 0
\(149\) −774.000 −0.425561 −0.212780 − 0.977100i \(-0.568252\pi\)
−0.212780 + 0.977100i \(0.568252\pi\)
\(150\) 0 0
\(151\) −293.000 −0.157907 −0.0789536 − 0.996878i \(-0.525158\pi\)
−0.0789536 + 0.996878i \(0.525158\pi\)
\(152\) 0 0
\(153\) 702.000 0.370937
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1729.00 −0.878912 −0.439456 − 0.898264i \(-0.644829\pi\)
−0.439456 + 0.898264i \(0.644829\pi\)
\(158\) 0 0
\(159\) −1656.00 −0.825971
\(160\) 0 0
\(161\) 3450.00 1.68881
\(162\) 0 0
\(163\) 1123.00 0.539633 0.269816 − 0.962912i \(-0.413037\pi\)
0.269816 + 0.962912i \(0.413037\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1200.00 −0.556041 −0.278020 − 0.960575i \(-0.589678\pi\)
−0.278020 + 0.960575i \(0.589678\pi\)
\(168\) 0 0
\(169\) −1356.00 −0.617205
\(170\) 0 0
\(171\) −1341.00 −0.599701
\(172\) 0 0
\(173\) −1734.00 −0.762044 −0.381022 − 0.924566i \(-0.624428\pi\)
−0.381022 + 0.924566i \(0.624428\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 810.000 0.343974
\(178\) 0 0
\(179\) −2586.00 −1.07981 −0.539907 − 0.841725i \(-0.681541\pi\)
−0.539907 + 0.841725i \(0.681541\pi\)
\(180\) 0 0
\(181\) −3931.00 −1.61430 −0.807152 − 0.590344i \(-0.798992\pi\)
−0.807152 + 0.590344i \(0.798992\pi\)
\(182\) 0 0
\(183\) 825.000 0.333255
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2340.00 0.915068
\(188\) 0 0
\(189\) −621.000 −0.239001
\(190\) 0 0
\(191\) −1566.00 −0.593255 −0.296628 − 0.954993i \(-0.595862\pi\)
−0.296628 + 0.954993i \(0.595862\pi\)
\(192\) 0 0
\(193\) 2291.00 0.854455 0.427227 − 0.904144i \(-0.359490\pi\)
0.427227 + 0.904144i \(0.359490\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2142.00 0.774676 0.387338 − 0.921938i \(-0.373395\pi\)
0.387338 + 0.921938i \(0.373395\pi\)
\(198\) 0 0
\(199\) 4903.00 1.74656 0.873278 − 0.487223i \(-0.161990\pi\)
0.873278 + 0.487223i \(0.161990\pi\)
\(200\) 0 0
\(201\) −2409.00 −0.845362
\(202\) 0 0
\(203\) 5382.00 1.86080
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1350.00 −0.453292
\(208\) 0 0
\(209\) −4470.00 −1.47941
\(210\) 0 0
\(211\) −605.000 −0.197393 −0.0986965 − 0.995118i \(-0.531467\pi\)
−0.0986965 + 0.995118i \(0.531467\pi\)
\(212\) 0 0
\(213\) −1980.00 −0.636936
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −4991.00 −1.56134
\(218\) 0 0
\(219\) −1938.00 −0.597981
\(220\) 0 0
\(221\) 2262.00 0.688500
\(222\) 0 0
\(223\) 145.000 0.0435422 0.0217711 − 0.999763i \(-0.493069\pi\)
0.0217711 + 0.999763i \(0.493069\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −2964.00 −0.866641 −0.433321 − 0.901240i \(-0.642658\pi\)
−0.433321 + 0.901240i \(0.642658\pi\)
\(228\) 0 0
\(229\) −5635.00 −1.62608 −0.813038 − 0.582211i \(-0.802188\pi\)
−0.813038 + 0.582211i \(0.802188\pi\)
\(230\) 0 0
\(231\) −2070.00 −0.589593
\(232\) 0 0
\(233\) 4164.00 1.17078 0.585392 − 0.810750i \(-0.300941\pi\)
0.585392 + 0.810750i \(0.300941\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −2976.00 −0.815662
\(238\) 0 0
\(239\) 1944.00 0.526138 0.263069 − 0.964777i \(-0.415265\pi\)
0.263069 + 0.964777i \(0.415265\pi\)
\(240\) 0 0
\(241\) 857.000 0.229063 0.114532 − 0.993420i \(-0.463463\pi\)
0.114532 + 0.993420i \(0.463463\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4321.00 −1.11311
\(248\) 0 0
\(249\) 2538.00 0.645941
\(250\) 0 0
\(251\) 3924.00 0.986776 0.493388 − 0.869809i \(-0.335758\pi\)
0.493388 + 0.869809i \(0.335758\pi\)
\(252\) 0 0
\(253\) −4500.00 −1.11823
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2844.00 −0.690287 −0.345144 − 0.938550i \(-0.612170\pi\)
−0.345144 + 0.938550i \(0.612170\pi\)
\(258\) 0 0
\(259\) −3358.00 −0.805621
\(260\) 0 0
\(261\) −2106.00 −0.499456
\(262\) 0 0
\(263\) 6060.00 1.42082 0.710410 − 0.703788i \(-0.248510\pi\)
0.710410 + 0.703788i \(0.248510\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −4464.00 −1.02319
\(268\) 0 0
\(269\) 3906.00 0.885327 0.442664 − 0.896688i \(-0.354034\pi\)
0.442664 + 0.896688i \(0.354034\pi\)
\(270\) 0 0
\(271\) −2144.00 −0.480586 −0.240293 − 0.970700i \(-0.577243\pi\)
−0.240293 + 0.970700i \(0.577243\pi\)
\(272\) 0 0
\(273\) −2001.00 −0.443612
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 2321.00 0.503449 0.251725 − 0.967799i \(-0.419002\pi\)
0.251725 + 0.967799i \(0.419002\pi\)
\(278\) 0 0
\(279\) 1953.00 0.419079
\(280\) 0 0
\(281\) −6822.00 −1.44828 −0.724140 − 0.689654i \(-0.757763\pi\)
−0.724140 + 0.689654i \(0.757763\pi\)
\(282\) 0 0
\(283\) −4049.00 −0.850488 −0.425244 − 0.905079i \(-0.639812\pi\)
−0.425244 + 0.905079i \(0.639812\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3588.00 0.737955
\(288\) 0 0
\(289\) 1171.00 0.238347
\(290\) 0 0
\(291\) −957.000 −0.192785
\(292\) 0 0
\(293\) 2238.00 0.446230 0.223115 − 0.974792i \(-0.428377\pi\)
0.223115 + 0.974792i \(0.428377\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 810.000 0.158252
\(298\) 0 0
\(299\) −4350.00 −0.841361
\(300\) 0 0
\(301\) −9959.00 −1.90707
\(302\) 0 0
\(303\) −2376.00 −0.450487
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −1385.00 −0.257479 −0.128740 − 0.991678i \(-0.541093\pi\)
−0.128740 + 0.991678i \(0.541093\pi\)
\(308\) 0 0
\(309\) −2436.00 −0.448476
\(310\) 0 0
\(311\) 5670.00 1.03381 0.516907 − 0.856042i \(-0.327083\pi\)
0.516907 + 0.856042i \(0.327083\pi\)
\(312\) 0 0
\(313\) −421.000 −0.0760266 −0.0380133 − 0.999277i \(-0.512103\pi\)
−0.0380133 + 0.999277i \(0.512103\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9984.00 1.76895 0.884475 − 0.466587i \(-0.154517\pi\)
0.884475 + 0.466587i \(0.154517\pi\)
\(318\) 0 0
\(319\) −7020.00 −1.23211
\(320\) 0 0
\(321\) 4248.00 0.738630
\(322\) 0 0
\(323\) −11622.0 −2.00206
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −165.000 −0.0279037
\(328\) 0 0
\(329\) 690.000 0.115626
\(330\) 0 0
\(331\) 4228.00 0.702090 0.351045 − 0.936359i \(-0.385826\pi\)
0.351045 + 0.936359i \(0.385826\pi\)
\(332\) 0 0
\(333\) 1314.00 0.216237
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 5393.00 0.871737 0.435869 − 0.900010i \(-0.356441\pi\)
0.435869 + 0.900010i \(0.356441\pi\)
\(338\) 0 0
\(339\) 4212.00 0.674821
\(340\) 0 0
\(341\) 6510.00 1.03383
\(342\) 0 0
\(343\) 3611.00 0.568442
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7914.00 1.22434 0.612170 − 0.790726i \(-0.290297\pi\)
0.612170 + 0.790726i \(0.290297\pi\)
\(348\) 0 0
\(349\) 1010.00 0.154911 0.0774557 − 0.996996i \(-0.475320\pi\)
0.0774557 + 0.996996i \(0.475320\pi\)
\(350\) 0 0
\(351\) 783.000 0.119070
\(352\) 0 0
\(353\) 4722.00 0.711974 0.355987 − 0.934491i \(-0.384145\pi\)
0.355987 + 0.934491i \(0.384145\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −5382.00 −0.797887
\(358\) 0 0
\(359\) −6204.00 −0.912074 −0.456037 − 0.889961i \(-0.650732\pi\)
−0.456037 + 0.889961i \(0.650732\pi\)
\(360\) 0 0
\(361\) 15342.0 2.23677
\(362\) 0 0
\(363\) −1293.00 −0.186956
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −1361.00 −0.193579 −0.0967897 − 0.995305i \(-0.530857\pi\)
−0.0967897 + 0.995305i \(0.530857\pi\)
\(368\) 0 0
\(369\) −1404.00 −0.198074
\(370\) 0 0
\(371\) 12696.0 1.77667
\(372\) 0 0
\(373\) −913.000 −0.126738 −0.0633691 − 0.997990i \(-0.520185\pi\)
−0.0633691 + 0.997990i \(0.520185\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6786.00 −0.927047
\(378\) 0 0
\(379\) 8881.00 1.20366 0.601829 − 0.798625i \(-0.294439\pi\)
0.601829 + 0.798625i \(0.294439\pi\)
\(380\) 0 0
\(381\) −3840.00 −0.516350
\(382\) 0 0
\(383\) −5460.00 −0.728441 −0.364221 − 0.931313i \(-0.618665\pi\)
−0.364221 + 0.931313i \(0.618665\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3897.00 0.511875
\(388\) 0 0
\(389\) −13884.0 −1.80963 −0.904816 − 0.425803i \(-0.859992\pi\)
−0.904816 + 0.425803i \(0.859992\pi\)
\(390\) 0 0
\(391\) −11700.0 −1.51328
\(392\) 0 0
\(393\) −1440.00 −0.184831
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −3781.00 −0.477992 −0.238996 − 0.971021i \(-0.576818\pi\)
−0.238996 + 0.971021i \(0.576818\pi\)
\(398\) 0 0
\(399\) 10281.0 1.28996
\(400\) 0 0
\(401\) 9024.00 1.12378 0.561892 − 0.827211i \(-0.310074\pi\)
0.561892 + 0.827211i \(0.310074\pi\)
\(402\) 0 0
\(403\) 6293.00 0.777858
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4380.00 0.533436
\(408\) 0 0
\(409\) 14789.0 1.78794 0.893972 − 0.448123i \(-0.147907\pi\)
0.893972 + 0.448123i \(0.147907\pi\)
\(410\) 0 0
\(411\) −846.000 −0.101533
\(412\) 0 0
\(413\) −6210.00 −0.739889
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −4812.00 −0.565095
\(418\) 0 0
\(419\) −9840.00 −1.14729 −0.573646 − 0.819103i \(-0.694472\pi\)
−0.573646 + 0.819103i \(0.694472\pi\)
\(420\) 0 0
\(421\) 5510.00 0.637865 0.318932 − 0.947778i \(-0.396676\pi\)
0.318932 + 0.947778i \(0.396676\pi\)
\(422\) 0 0
\(423\) −270.000 −0.0310351
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −6325.00 −0.716834
\(428\) 0 0
\(429\) 2610.00 0.293734
\(430\) 0 0
\(431\) −11070.0 −1.23718 −0.618588 − 0.785715i \(-0.712295\pi\)
−0.618588 + 0.785715i \(0.712295\pi\)
\(432\) 0 0
\(433\) −12133.0 −1.34659 −0.673297 − 0.739373i \(-0.735122\pi\)
−0.673297 + 0.739373i \(0.735122\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 22350.0 2.44656
\(438\) 0 0
\(439\) 1873.00 0.203630 0.101815 − 0.994803i \(-0.467535\pi\)
0.101815 + 0.994803i \(0.467535\pi\)
\(440\) 0 0
\(441\) 1674.00 0.180758
\(442\) 0 0
\(443\) 576.000 0.0617756 0.0308878 − 0.999523i \(-0.490167\pi\)
0.0308878 + 0.999523i \(0.490167\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −2322.00 −0.245698
\(448\) 0 0
\(449\) −4884.00 −0.513341 −0.256671 − 0.966499i \(-0.582626\pi\)
−0.256671 + 0.966499i \(0.582626\pi\)
\(450\) 0 0
\(451\) −4680.00 −0.488631
\(452\) 0 0
\(453\) −879.000 −0.0911678
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −15802.0 −1.61748 −0.808738 − 0.588169i \(-0.799849\pi\)
−0.808738 + 0.588169i \(0.799849\pi\)
\(458\) 0 0
\(459\) 2106.00 0.214160
\(460\) 0 0
\(461\) −15360.0 −1.55181 −0.775907 − 0.630847i \(-0.782708\pi\)
−0.775907 + 0.630847i \(0.782708\pi\)
\(462\) 0 0
\(463\) −1712.00 −0.171843 −0.0859216 − 0.996302i \(-0.527383\pi\)
−0.0859216 + 0.996302i \(0.527383\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 16278.0 1.61297 0.806484 − 0.591256i \(-0.201368\pi\)
0.806484 + 0.591256i \(0.201368\pi\)
\(468\) 0 0
\(469\) 18469.0 1.81838
\(470\) 0 0
\(471\) −5187.00 −0.507440
\(472\) 0 0
\(473\) 12990.0 1.26275
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −4968.00 −0.476874
\(478\) 0 0
\(479\) 14766.0 1.40851 0.704254 − 0.709948i \(-0.251281\pi\)
0.704254 + 0.709948i \(0.251281\pi\)
\(480\) 0 0
\(481\) 4234.00 0.401359
\(482\) 0 0
\(483\) 10350.0 0.975034
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 3319.00 0.308826 0.154413 − 0.988006i \(-0.450651\pi\)
0.154413 + 0.988006i \(0.450651\pi\)
\(488\) 0 0
\(489\) 3369.00 0.311557
\(490\) 0 0
\(491\) −11064.0 −1.01693 −0.508464 − 0.861083i \(-0.669786\pi\)
−0.508464 + 0.861083i \(0.669786\pi\)
\(492\) 0 0
\(493\) −18252.0 −1.66740
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 15180.0 1.37005
\(498\) 0 0
\(499\) 14131.0 1.26772 0.633858 − 0.773449i \(-0.281470\pi\)
0.633858 + 0.773449i \(0.281470\pi\)
\(500\) 0 0
\(501\) −3600.00 −0.321030
\(502\) 0 0
\(503\) −11988.0 −1.06266 −0.531331 − 0.847165i \(-0.678308\pi\)
−0.531331 + 0.847165i \(0.678308\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −4068.00 −0.356344
\(508\) 0 0
\(509\) 10806.0 0.940997 0.470499 − 0.882401i \(-0.344074\pi\)
0.470499 + 0.882401i \(0.344074\pi\)
\(510\) 0 0
\(511\) 14858.0 1.28626
\(512\) 0 0
\(513\) −4023.00 −0.346237
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −900.000 −0.0765608
\(518\) 0 0
\(519\) −5202.00 −0.439966
\(520\) 0 0
\(521\) 22578.0 1.89858 0.949290 − 0.314402i \(-0.101804\pi\)
0.949290 + 0.314402i \(0.101804\pi\)
\(522\) 0 0
\(523\) −12065.0 −1.00873 −0.504365 − 0.863491i \(-0.668273\pi\)
−0.504365 + 0.863491i \(0.668273\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 16926.0 1.39907
\(528\) 0 0
\(529\) 10333.0 0.849264
\(530\) 0 0
\(531\) 2430.00 0.198593
\(532\) 0 0
\(533\) −4524.00 −0.367648
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −7758.00 −0.623431
\(538\) 0 0
\(539\) 5580.00 0.445914
\(540\) 0 0
\(541\) −12055.0 −0.958013 −0.479006 − 0.877811i \(-0.659003\pi\)
−0.479006 + 0.877811i \(0.659003\pi\)
\(542\) 0 0
\(543\) −11793.0 −0.932019
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −6176.00 −0.482754 −0.241377 − 0.970431i \(-0.577599\pi\)
−0.241377 + 0.970431i \(0.577599\pi\)
\(548\) 0 0
\(549\) 2475.00 0.192405
\(550\) 0 0
\(551\) 34866.0 2.69572
\(552\) 0 0
\(553\) 22816.0 1.75449
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8274.00 0.629409 0.314704 − 0.949190i \(-0.398095\pi\)
0.314704 + 0.949190i \(0.398095\pi\)
\(558\) 0 0
\(559\) 12557.0 0.950098
\(560\) 0 0
\(561\) 7020.00 0.528315
\(562\) 0 0
\(563\) −966.000 −0.0723127 −0.0361563 − 0.999346i \(-0.511511\pi\)
−0.0361563 + 0.999346i \(0.511511\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −1863.00 −0.137987
\(568\) 0 0
\(569\) 19002.0 1.40001 0.700005 − 0.714138i \(-0.253181\pi\)
0.700005 + 0.714138i \(0.253181\pi\)
\(570\) 0 0
\(571\) −8645.00 −0.633594 −0.316797 − 0.948493i \(-0.602607\pi\)
−0.316797 + 0.948493i \(0.602607\pi\)
\(572\) 0 0
\(573\) −4698.00 −0.342516
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 10931.0 0.788672 0.394336 − 0.918966i \(-0.370975\pi\)
0.394336 + 0.918966i \(0.370975\pi\)
\(578\) 0 0
\(579\) 6873.00 0.493320
\(580\) 0 0
\(581\) −19458.0 −1.38942
\(582\) 0 0
\(583\) −16560.0 −1.17641
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8904.00 −0.626077 −0.313039 − 0.949740i \(-0.601347\pi\)
−0.313039 + 0.949740i \(0.601347\pi\)
\(588\) 0 0
\(589\) −32333.0 −2.26190
\(590\) 0 0
\(591\) 6426.00 0.447259
\(592\) 0 0
\(593\) 8820.00 0.610782 0.305391 − 0.952227i \(-0.401213\pi\)
0.305391 + 0.952227i \(0.401213\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 14709.0 1.00837
\(598\) 0 0
\(599\) −9804.00 −0.668749 −0.334374 − 0.942440i \(-0.608525\pi\)
−0.334374 + 0.942440i \(0.608525\pi\)
\(600\) 0 0
\(601\) −23437.0 −1.59071 −0.795354 − 0.606146i \(-0.792715\pi\)
−0.795354 + 0.606146i \(0.792715\pi\)
\(602\) 0 0
\(603\) −7227.00 −0.488070
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −2648.00 −0.177066 −0.0885330 − 0.996073i \(-0.528218\pi\)
−0.0885330 + 0.996073i \(0.528218\pi\)
\(608\) 0 0
\(609\) 16146.0 1.07433
\(610\) 0 0
\(611\) −870.000 −0.0576046
\(612\) 0 0
\(613\) 794.000 0.0523154 0.0261577 − 0.999658i \(-0.491673\pi\)
0.0261577 + 0.999658i \(0.491673\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 18720.0 1.22146 0.610728 − 0.791840i \(-0.290877\pi\)
0.610728 + 0.791840i \(0.290877\pi\)
\(618\) 0 0
\(619\) 8959.00 0.581733 0.290866 − 0.956764i \(-0.406056\pi\)
0.290866 + 0.956764i \(0.406056\pi\)
\(620\) 0 0
\(621\) −4050.00 −0.261708
\(622\) 0 0
\(623\) 34224.0 2.20089
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −13410.0 −0.854137
\(628\) 0 0
\(629\) 11388.0 0.721891
\(630\) 0 0
\(631\) 12373.0 0.780604 0.390302 − 0.920687i \(-0.372371\pi\)
0.390302 + 0.920687i \(0.372371\pi\)
\(632\) 0 0
\(633\) −1815.00 −0.113965
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 5394.00 0.335507
\(638\) 0 0
\(639\) −5940.00 −0.367735
\(640\) 0 0
\(641\) 24900.0 1.53431 0.767154 − 0.641463i \(-0.221672\pi\)
0.767154 + 0.641463i \(0.221672\pi\)
\(642\) 0 0
\(643\) 14668.0 0.899610 0.449805 − 0.893127i \(-0.351493\pi\)
0.449805 + 0.893127i \(0.351493\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 10788.0 0.655518 0.327759 − 0.944761i \(-0.393707\pi\)
0.327759 + 0.944761i \(0.393707\pi\)
\(648\) 0 0
\(649\) 8100.00 0.489912
\(650\) 0 0
\(651\) −14973.0 −0.901441
\(652\) 0 0
\(653\) −14214.0 −0.851817 −0.425909 − 0.904766i \(-0.640046\pi\)
−0.425909 + 0.904766i \(0.640046\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −5814.00 −0.345245
\(658\) 0 0
\(659\) 588.000 0.0347576 0.0173788 − 0.999849i \(-0.494468\pi\)
0.0173788 + 0.999849i \(0.494468\pi\)
\(660\) 0 0
\(661\) −3166.00 −0.186298 −0.0931491 − 0.995652i \(-0.529693\pi\)
−0.0931491 + 0.995652i \(0.529693\pi\)
\(662\) 0 0
\(663\) 6786.00 0.397506
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 35100.0 2.03760
\(668\) 0 0
\(669\) 435.000 0.0251391
\(670\) 0 0
\(671\) 8250.00 0.474646
\(672\) 0 0
\(673\) 9182.00 0.525914 0.262957 − 0.964808i \(-0.415302\pi\)
0.262957 + 0.964808i \(0.415302\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 11742.0 0.666590 0.333295 − 0.942823i \(-0.391839\pi\)
0.333295 + 0.942823i \(0.391839\pi\)
\(678\) 0 0
\(679\) 7337.00 0.414681
\(680\) 0 0
\(681\) −8892.00 −0.500356
\(682\) 0 0
\(683\) 6024.00 0.337485 0.168742 − 0.985660i \(-0.446029\pi\)
0.168742 + 0.985660i \(0.446029\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −16905.0 −0.938815
\(688\) 0 0
\(689\) −16008.0 −0.885132
\(690\) 0 0
\(691\) −9344.00 −0.514418 −0.257209 − 0.966356i \(-0.582803\pi\)
−0.257209 + 0.966356i \(0.582803\pi\)
\(692\) 0 0
\(693\) −6210.00 −0.340402
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −12168.0 −0.661257
\(698\) 0 0
\(699\) 12492.0 0.675953
\(700\) 0 0
\(701\) 21234.0 1.14408 0.572038 − 0.820227i \(-0.306153\pi\)
0.572038 + 0.820227i \(0.306153\pi\)
\(702\) 0 0
\(703\) −21754.0 −1.16709
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 18216.0 0.969000
\(708\) 0 0
\(709\) −1723.00 −0.0912675 −0.0456337 − 0.998958i \(-0.514531\pi\)
−0.0456337 + 0.998958i \(0.514531\pi\)
\(710\) 0 0
\(711\) −8928.00 −0.470923
\(712\) 0 0
\(713\) −32550.0 −1.70969
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 5832.00 0.303766
\(718\) 0 0
\(719\) −18510.0 −0.960093 −0.480046 − 0.877243i \(-0.659380\pi\)
−0.480046 + 0.877243i \(0.659380\pi\)
\(720\) 0 0
\(721\) 18676.0 0.964675
\(722\) 0 0
\(723\) 2571.00 0.132250
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1009.00 0.0514742 0.0257371 − 0.999669i \(-0.491807\pi\)
0.0257371 + 0.999669i \(0.491807\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 33774.0 1.70886
\(732\) 0 0
\(733\) −21994.0 −1.10828 −0.554138 − 0.832425i \(-0.686952\pi\)
−0.554138 + 0.832425i \(0.686952\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −24090.0 −1.20403
\(738\) 0 0
\(739\) 13948.0 0.694297 0.347148 − 0.937810i \(-0.387150\pi\)
0.347148 + 0.937810i \(0.387150\pi\)
\(740\) 0 0
\(741\) −12963.0 −0.642655
\(742\) 0 0
\(743\) 26508.0 1.30886 0.654431 − 0.756122i \(-0.272908\pi\)
0.654431 + 0.756122i \(0.272908\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 7614.00 0.372934
\(748\) 0 0
\(749\) −32568.0 −1.58880
\(750\) 0 0
\(751\) 1600.00 0.0777428 0.0388714 − 0.999244i \(-0.487624\pi\)
0.0388714 + 0.999244i \(0.487624\pi\)
\(752\) 0 0
\(753\) 11772.0 0.569715
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 30101.0 1.44523 0.722615 − 0.691250i \(-0.242940\pi\)
0.722615 + 0.691250i \(0.242940\pi\)
\(758\) 0 0
\(759\) −13500.0 −0.645611
\(760\) 0 0
\(761\) 35628.0 1.69713 0.848564 − 0.529093i \(-0.177468\pi\)
0.848564 + 0.529093i \(0.177468\pi\)
\(762\) 0 0
\(763\) 1265.00 0.0600211
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 7830.00 0.368611
\(768\) 0 0
\(769\) −12517.0 −0.586963 −0.293482 − 0.955965i \(-0.594814\pi\)
−0.293482 + 0.955965i \(0.594814\pi\)
\(770\) 0 0
\(771\) −8532.00 −0.398538
\(772\) 0 0
\(773\) 14124.0 0.657186 0.328593 − 0.944472i \(-0.393426\pi\)
0.328593 + 0.944472i \(0.393426\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −10074.0 −0.465126
\(778\) 0 0
\(779\) 23244.0 1.06907
\(780\) 0 0
\(781\) −19800.0 −0.907170
\(782\) 0 0
\(783\) −6318.00 −0.288361
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −40433.0 −1.83136 −0.915680 − 0.401907i \(-0.868347\pi\)
−0.915680 + 0.401907i \(0.868347\pi\)
\(788\) 0 0
\(789\) 18180.0 0.820311
\(790\) 0 0
\(791\) −32292.0 −1.45154
\(792\) 0 0
\(793\) 7975.00 0.357126
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −27300.0 −1.21332 −0.606660 − 0.794962i \(-0.707491\pi\)
−0.606660 + 0.794962i \(0.707491\pi\)
\(798\) 0 0
\(799\) −2340.00 −0.103609
\(800\) 0 0
\(801\) −13392.0 −0.590740
\(802\) 0 0
\(803\) −19380.0 −0.851688
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 11718.0 0.511144
\(808\) 0 0
\(809\) −2856.00 −0.124118 −0.0620591 − 0.998072i \(-0.519767\pi\)
−0.0620591 + 0.998072i \(0.519767\pi\)
\(810\) 0 0
\(811\) 12619.0 0.546379 0.273189 − 0.961960i \(-0.411921\pi\)
0.273189 + 0.961960i \(0.411921\pi\)
\(812\) 0 0
\(813\) −6432.00 −0.277466
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −64517.0 −2.76275
\(818\) 0 0
\(819\) −6003.00 −0.256119
\(820\) 0 0
\(821\) −29082.0 −1.23626 −0.618130 − 0.786076i \(-0.712109\pi\)
−0.618130 + 0.786076i \(0.712109\pi\)
\(822\) 0 0
\(823\) −10235.0 −0.433499 −0.216749 − 0.976227i \(-0.569545\pi\)
−0.216749 + 0.976227i \(0.569545\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −26976.0 −1.13428 −0.567139 − 0.823622i \(-0.691950\pi\)
−0.567139 + 0.823622i \(0.691950\pi\)
\(828\) 0 0
\(829\) 37802.0 1.58374 0.791868 − 0.610692i \(-0.209109\pi\)
0.791868 + 0.610692i \(0.209109\pi\)
\(830\) 0 0
\(831\) 6963.00 0.290666
\(832\) 0 0
\(833\) 14508.0 0.603448
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 5859.00 0.241955
\(838\) 0 0
\(839\) 16974.0 0.698460 0.349230 − 0.937037i \(-0.386443\pi\)
0.349230 + 0.937037i \(0.386443\pi\)
\(840\) 0 0
\(841\) 30367.0 1.24511
\(842\) 0 0
\(843\) −20466.0 −0.836164
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 9913.00 0.402143
\(848\) 0 0
\(849\) −12147.0 −0.491029
\(850\) 0 0
\(851\) −21900.0 −0.882165
\(852\) 0 0
\(853\) −24937.0 −1.00097 −0.500485 − 0.865745i \(-0.666845\pi\)
−0.500485 + 0.865745i \(0.666845\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 15756.0 0.628022 0.314011 − 0.949419i \(-0.398327\pi\)
0.314011 + 0.949419i \(0.398327\pi\)
\(858\) 0 0
\(859\) −38144.0 −1.51508 −0.757542 − 0.652787i \(-0.773600\pi\)
−0.757542 + 0.652787i \(0.773600\pi\)
\(860\) 0 0
\(861\) 10764.0 0.426058
\(862\) 0 0
\(863\) −5448.00 −0.214892 −0.107446 − 0.994211i \(-0.534267\pi\)
−0.107446 + 0.994211i \(0.534267\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 3513.00 0.137610
\(868\) 0 0
\(869\) −29760.0 −1.16172
\(870\) 0 0
\(871\) −23287.0 −0.905913
\(872\) 0 0
\(873\) −2871.00 −0.111304
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 21191.0 0.815928 0.407964 − 0.912998i \(-0.366239\pi\)
0.407964 + 0.912998i \(0.366239\pi\)
\(878\) 0 0
\(879\) 6714.00 0.257631
\(880\) 0 0
\(881\) 18216.0 0.696609 0.348305 − 0.937381i \(-0.386758\pi\)
0.348305 + 0.937381i \(0.386758\pi\)
\(882\) 0 0
\(883\) −12767.0 −0.486573 −0.243286 − 0.969955i \(-0.578225\pi\)
−0.243286 + 0.969955i \(0.578225\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −11010.0 −0.416775 −0.208388 − 0.978046i \(-0.566822\pi\)
−0.208388 + 0.978046i \(0.566822\pi\)
\(888\) 0 0
\(889\) 29440.0 1.11067
\(890\) 0 0
\(891\) 2430.00 0.0913671
\(892\) 0 0
\(893\) 4470.00 0.167506
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −13050.0 −0.485760
\(898\) 0 0
\(899\) −50778.0 −1.88381
\(900\) 0 0
\(901\) −43056.0 −1.59201
\(902\) 0 0
\(903\) −29877.0 −1.10105
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −22772.0 −0.833662 −0.416831 − 0.908984i \(-0.636859\pi\)
−0.416831 + 0.908984i \(0.636859\pi\)
\(908\) 0 0
\(909\) −7128.00 −0.260089
\(910\) 0 0
\(911\) −29802.0 −1.08385 −0.541923 − 0.840428i \(-0.682304\pi\)
−0.541923 + 0.840428i \(0.682304\pi\)
\(912\) 0 0
\(913\) 25380.0 0.919995
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 11040.0 0.397571
\(918\) 0 0
\(919\) −48941.0 −1.75671 −0.878354 − 0.478011i \(-0.841358\pi\)
−0.878354 + 0.478011i \(0.841358\pi\)
\(920\) 0 0
\(921\) −4155.00 −0.148656
\(922\) 0 0
\(923\) −19140.0 −0.682558
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −7308.00 −0.258928
\(928\) 0 0
\(929\) 31026.0 1.09573 0.547863 − 0.836568i \(-0.315441\pi\)
0.547863 + 0.836568i \(0.315441\pi\)
\(930\) 0 0
\(931\) −27714.0 −0.975607
\(932\) 0 0
\(933\) 17010.0 0.596873
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 11183.0 0.389896 0.194948 − 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(938\) 0 0
\(939\) −1263.00 −0.0438940
\(940\) 0 0
\(941\) −2562.00 −0.0887554 −0.0443777 − 0.999015i \(-0.514130\pi\)
−0.0443777 + 0.999015i \(0.514130\pi\)
\(942\) 0 0
\(943\) 23400.0 0.808069
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −7638.00 −0.262093 −0.131046 − 0.991376i \(-0.541834\pi\)
−0.131046 + 0.991376i \(0.541834\pi\)
\(948\) 0 0
\(949\) −18734.0 −0.640813
\(950\) 0 0
\(951\) 29952.0 1.02130
\(952\) 0 0
\(953\) 51432.0 1.74821 0.874106 − 0.485735i \(-0.161448\pi\)
0.874106 + 0.485735i \(0.161448\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −21060.0 −0.711362
\(958\) 0 0
\(959\) 6486.00 0.218398
\(960\) 0 0
\(961\) 17298.0 0.580645
\(962\) 0 0
\(963\) 12744.0 0.426448
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −39728.0 −1.32116 −0.660582 − 0.750754i \(-0.729691\pi\)
−0.660582 + 0.750754i \(0.729691\pi\)
\(968\) 0 0
\(969\) −34866.0 −1.15589
\(970\) 0 0
\(971\) 47946.0 1.58461 0.792307 − 0.610123i \(-0.208880\pi\)
0.792307 + 0.610123i \(0.208880\pi\)
\(972\) 0 0
\(973\) 36892.0 1.21552
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −22326.0 −0.731087 −0.365544 − 0.930794i \(-0.619117\pi\)
−0.365544 + 0.930794i \(0.619117\pi\)
\(978\) 0 0
\(979\) −44640.0 −1.45730
\(980\) 0 0
\(981\) −495.000 −0.0161102
\(982\) 0 0
\(983\) 48468.0 1.57262 0.786312 − 0.617830i \(-0.211988\pi\)
0.786312 + 0.617830i \(0.211988\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 2070.00 0.0667567
\(988\) 0 0
\(989\) −64950.0 −2.08826
\(990\) 0 0
\(991\) 25141.0 0.805883 0.402942 − 0.915226i \(-0.367988\pi\)
0.402942 + 0.915226i \(0.367988\pi\)
\(992\) 0 0
\(993\) 12684.0 0.405352
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −35422.0 −1.12520 −0.562601 − 0.826729i \(-0.690199\pi\)
−0.562601 + 0.826729i \(0.690199\pi\)
\(998\) 0 0
\(999\) 3942.00 0.124844
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1200.4.a.v.1.1 1
4.3 odd 2 150.4.a.g.1.1 yes 1
5.2 odd 4 1200.4.f.q.49.1 2
5.3 odd 4 1200.4.f.q.49.2 2
5.4 even 2 1200.4.a.r.1.1 1
12.11 even 2 450.4.a.i.1.1 1
20.3 even 4 150.4.c.b.49.1 2
20.7 even 4 150.4.c.b.49.2 2
20.19 odd 2 150.4.a.c.1.1 ✓ 1
60.23 odd 4 450.4.c.h.199.2 2
60.47 odd 4 450.4.c.h.199.1 2
60.59 even 2 450.4.a.l.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.4.a.c.1.1 ✓ 1 20.19 odd 2
150.4.a.g.1.1 yes 1 4.3 odd 2
150.4.c.b.49.1 2 20.3 even 4
150.4.c.b.49.2 2 20.7 even 4
450.4.a.i.1.1 1 12.11 even 2
450.4.a.l.1.1 1 60.59 even 2
450.4.c.h.199.1 2 60.47 odd 4
450.4.c.h.199.2 2 60.23 odd 4
1200.4.a.r.1.1 1 5.4 even 2
1200.4.a.v.1.1 1 1.1 even 1 trivial
1200.4.f.q.49.1 2 5.2 odd 4
1200.4.f.q.49.2 2 5.3 odd 4